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## Q. 3.11

Methane $(CH_{4})$ is the principal ingredient in natural gas, but significant concentrations of the hydrocarbon gases ethane $(C_{2}H_{6})$ and propane $(C_{3}H_{8})$ are also present in most natural gas samples. Write a balanced chemical equation describing the complete combustion of $C_{2}H_{6}$.

## Verified Solution

Collect, Organize, and Analyze We need to write a balanced chemical equation for the combustion of $C_{2}H_{6}$. The products of complete combustion of hydrocarbons are carbon dioxide and water.

Solve The preliminary expression with single particles of all known reactants and products describing the combustion of ethane is

$C_{2}H_{6}(g)+O_{2}(g)\rightarrow CO_{2}(g)+H_{2}O(g)$

 Element Reactant Side Product Side Balanced? C 2 1 H 6 2 O 2 2+1-3

Because this reaction is between oxygen and a hydrocarbon, we balance C first, then H, then O. Balance the carbon atoms first by giving $CO_{2}$ in the product a coefficient of 2:

_ $C_{2}H_{6}(g)+$ _$O_{2}(g)\rightarrow \underline{2} CO_{2}(g)+$ _ $H_{2}O(g)$

 Element Reactant Side Product Side Balanced? C 2 2×1-2 H 6 2 O 2 (2×2)+1-5

Then balance the hydrogen atoms by giving $H_{2}O$ a coefficient of 3:

_ $C_{2}H_{6}(g)+$ _$O_{2}(g)\rightarrow \underline{2} CO_{2}(g)+\underline{3} H_{2}O(g)$

 Element Reactant Side Product Side Balanced? C 2 2×1-2 H 6 3×2-6 O 2 (2×2)+(3×1)-7

At this stage, the oxygen atoms cannot be balanced with a simple whole-number coefficient for $O_{2}$; we need $\frac{7}{2}O_{2}$. However, if we give $O_{2}$ a coefficient of 7 and double the coefficients for ethane, carbon dioxide, and water, we can write

$\underline{2}C_{2}H_{6}(g)+ \underline{7}O_{2}(g)\rightarrow \underline{4} CO_{2}(g)+\underline{6} H_{2}O(g)$

 Element Reactant Side Product Side Balanced? C 2×2-4 4×1-4 H 2×6-12 6×2-12 O 7×2-14 (4×2)+(6×1)-14

This equation is balanced.

Think About It Balancing chemical equations for combustion reactions of hydrocarbons often requires several iterations of the coefficients before all of the elements are balanced.